[Lynne]

Try this:
Create a new template called "memberinfo_block_yours" with this (Just copied from memberinfo_block_ministats):

 	<!-- Your new block -->
<div class="alt1 block_row">
	<table cellpadding="0" cellspacing="0" border="0">
	<tr valign="top">
		<td width="100%">
Your stuff here
		</td>
	</tr>
	</table>
</div>
<!-- / Your new block -->

Create a plugin at hook location "member_build_blocks_start" with this:

PHP Code:

eval('$template_hook[profile_right_first] .= "' . fetch_template('memberinfo_block_yours') . '";'); 


I have NOT tested this.